This is what I think I understand is going on:
Total hardness is a measure of Magnesium + Calcium including the hardness that doesn't boil out, and therefore isn't very useful as a figure (even though that's the only one that Thames Water are giving me).
Alkalinity is used as a measure of bicarbonates and carbonates.
Residual alkalinity is used to describe the effect whereby calcium and magnesium in the mash releases H+ from the grain to neutralise alkalinity in the mash.
So to know what your mash pH is going to be you need to somehow measure calcium, magnesium and alkalinity.
When you do the methyl orange test you're testing alkalinity (bicarb and carbonates) by virtue of the buffering effect of these compounds but then you still need to know Ca+Mg (or have estimates for them) to work out your residual alkalinity (and therefore mash pH and what treatments to use).
So- assuming this is correct, I can use an alkainity test kit to work out my bicarbs and carbs and providing I get a measure of Ca+Mg from TW (or cough up the £30 a private lab has quoted me to test PPM for bicarb, ca + mg from a water sample) I can work out what I need to do to the water to make my LP clone

Why I get confused is I can't help but feel that alkalinity and pH should be closely related. But I suppose the H+ content (pH) won't necessarily be ONLY offset by the alkalinity....
